Graph the function f(x)=x^2+6 as a translation of g(x)=x^2 Use the graphing tool to graph the function as a solid curve. Click to enlarge graph

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Graph the function f(x)=x^2+6 as a translation of g(x)=x^2 Use the graphing tool to graph the function as a solid curve. Click to enlarge graph

Answer 1

To graph \( f(x) = x^2 + 6 \) as a translation of \( g(x) = x^2 \): 1. Start with the graph of \( g(x) = x^2 \), which is a parabola opening upwards with its vertex at the origin (0,0). 2. Shift the entire graph of \( g(x) = x^2 \) vertically upward by 6 units. 3. The new vertex of the parabola will be at (0, 6). The graph of \( f(x) = x^2 + 6 \) will be a parabola opening upwards with its vertex at (0, 6).

Answer 2

The function \( f(x) = x^2 + 6 \) is a vertical translation of the function \( g(x) = x^2 \). Specifically, it is shifted 6 units up along the y-axis. The shape of the graph remains the same as \( g(x) = x^2 \), but every point on the graph is moved up by 6 units.

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Graph the function f(x)=x^2+6 as a translation of g(x)=x^2 Use the graphing tool to graph the function as a solid curve. Click to enlarge graph

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